Extraction of fluorescent cell puncta by

We test our proposed segmenta-tion algorithm for extracting cell puncta with real image and compare the results with those obtained by other standard seg-mentation methods as well as a

Extraction of fluorescent cell puncta by adaptive fuzzy segmentation

Tuan D Pham1, ∗, Denis I Crane2,3, Tuan H Tran1 and Tam H Nguyen2,3

1 School of Computing and Information Technology, 2 Eskitis Institute for Cell and Molecular Therapies and 3 School of Biomolecular and Biomedical Sciences, Griffith University, Nathan Campus, QLD 4111, Australia

Received on November 24, 2003; revised on January 19, 2004; accepted on February 4, 2004 Advance Access publication April 1, 2004

ABSTRACT

Motivation: The discrimination and measurement of

fluorescent-labeled vesicles using microscopic analysis of

fixed cells presents a challenge for biologists interested in

quantifying the abundance, size and distribution of such

ves-icles in normal and abnormal cellular situations In the specific

application reported here, we were interested in quantifying

changes to the population of a major organelle, the

peroxi-some, in cells from normal control patients and from patients

with a defect in peroxisome biogenesis In the latter,

peroxi-somes are present as larger vesicular structures with a more

restricted cytoplasmic distribution Existing image processing

methods for extracting fluorescent cell puncta do not provide

useful results and therefore, there is a need to develop some

new approaches for dealing with such a task effectively

Results: We present an effective implementation of the fuzzy

c-means algorithm for extracting puncta (spots),

represent-ing fluorescent-labeled peroxisomes, which are subject to low

contrast We make use of the quadtree partition to enhance the

fuzzy c-means based segmentation and to disregard regions

which contain no target objects (peroxisomes) in order to

min-imize considerable time taken by the iterative process of the

fuzzy c-means algorithm We finally isolate touching

peroxi-somes by an aspect-ratio criterion The proposed approach

has been applied to extract peroxisomes contained in

sev-eral sets of color images and the results are superior to

those obtained from a number of standard techniques for spot

extraction

Availability: Image data and computer codes written in Matlab

are available upon request from the first author

Contact: t.pham@griffith.edu.au

INTRODUCTION

There are a number of recently developed methods for the

analysis of DNA microarray spots such as the

morphology-based method proposed by Angulo and Serra (2003), the

∗To whom correspondence should be addressed.

combinatorial image analysis by Glasbey and Ghazal (2003)

and the adaptive thresholding by Liew et al (2003) However,

these morphological and statistical thresholding methods are only effective for extracting DNA microarray spots having similar sizes and contained in gridded structures The main reasons for the unsuitable applications of these methods for the segmentation and extraction of biological images in this study is that these images contain very variable (i) spot sizes, (ii) intensity distributions and (iii) backgrounds Therefore, extraction of these fluorescent cell puncta using these meth-ods will lead to over/under-segmented results An associated

method for spot extraction has been developed by Xu et al.

(1999), which is based on double thresholding and contour-based curve fitting to segment the images of skin cancer This method is suitable for the segmentation of isolated spots whereas the problem we study herein is not restricted to such cases and its curve fitting technique can only approximate the spot areas, that may lead to a considerable error for the quantification of peroxisome abundance

In this paper, we present a segmentation method based

on the fuzzy c-means for dealing with the more challenging

application of extracting and measuring cell puncta images that exhibit low contrast and variable size and cellular distri-bution, including clustering The specific application used to test this method is an analysis of the population of peroxisomes

in human patient cell lines Previous findings have indicated

a change in the size, cytoplasmic distribution and potential clustering of these cellular organelles in different peroxisomal

diseases (Chang et al., 1999) We test our proposed

segmenta-tion algorithm for extracting cell puncta with real image and compare the results with those obtained by other standard seg-mentation methods as well as a current medical image analysis software for spot extraction

IMPLEMENTATION Cell culture and immunofluorescence microscopy

Skin fibroblast cell lines were cultured in Dulbecco’s modified Eagle’s medium (high glucose), supplemented with 10% fetal

bovine serum (FBS) and 100 mg/ml penicillin–100 µg/ml

streptomycin (Gibco BRL) Cells were processed for indirect

immunofluorescence as described previously (Maxwell et al.,

1999, 2002) and peroxisomes detected using a rabbit

anti-body to the peroxisomal membrane protein PEX14 and an

FITC-labeled goat antirabbit secondary antibody (Chemicon)

Cells were visualized using a Nikon Eclipse E800

fluor-escence microscope equipped with an FITC filter Images

were captured with a Photometrics Coolsnap CCD camera

(Roper Scientific) and processed using V++ Precision Digital

Imaging software (Digital Optics)

Fuzzy c-means algorithm

The fuzzy c-means (FCM) algorithm (Bezdek, 1981) seeks

to partition a dataset {x1, x2, , x m}, where xm =

(x m1, x m2, , x mk ) , m = 1, 2, , M, into a specified

number of fuzzy regions which are represented by the

corres-ponding cluster centers The degrees of each xmthat belong

to different clusters are characterized by the corresponding

fuzzy membership grades taking real values between 0 and 1

In principle, the FCM maximizes the following objective

function:

J (U, c1, , c N )=

N

y=1

M

m=1

µ α ym d ym2 , (1)

where M is the number of data points, N is the number of

clusters, U is the N × M fuzzy membership matrix, µ ym ∈

[0, 1] is the fuzzy membership grade that indicates the degree

xm belongs to the fuzzy region y, d ymis a distance measure

between cluster center cy and data point xm , and α ∈ [1, ∞)

is the fuzzy exponential weight

The computations of the cluster centers and the partition

matrix U are updated by an iterative procedure which is

described as follows:

(1) Given the degree of fuzziness α and initial

member-ship matrix U with random values of µ ym ∈ [0, 1]

subjected to

N

y=1

µ ym = 1, ∀m = 1, , M.

(2) Update initial cluster centers

cj+1

M

m=1µ α ymxm

M

m=1µ α ym

(3) Update fuzzy membership functions

N

z=1



d ym

d zm

2/(α −1), (3) where, using the L2norm, dymis given by

d ym= ||xm− cy||2

Fig 1 Original image A.

Fig 2 Segmentation of image A by Otsu’s thresholding.

(4) Compute the objective function according to Equa-tion (1) If it converges or its improvement over the previous iteration is below a certain threshold then stop the iterative process Otherwise, go to step 2

Estimating the number of clusters

Taking a first look at the image (412× 357) as shown in

Figure 1, there appear to be two classes to be segmented These two classes are the background pixels and the peroxi-some puncta If we apply the well-known Otsu’s thresholding method (Otsu, 1979) and the FCM, with the number of clusters

N = 2, to segment the gray image of Figure 1, we obtain

Figures 2 and 3 which are the results given by Otsu method and the FCM, respectively It can be seen that both results over-estimate the spot sizes and highlight noise and outliers These are due to the low contrast of the image and particularly the fluorescence around the peroxisome spots We therefore need

to add another cluster to represent the fluorescent-shadow

Fig 3 Segmentation of image A by FCM with two clusters.

Fig 4 Segmentation of image A by FCM with three clusters.

pixels, i.e the number of classes will now be three instead of

two As Otsu method only works for gray-scale images with

two classes, we now apply the FCM with N = 3 and obtain

another result as shown in Figure 4 This result shows some

improvement over that obtained by the FCM with N = 2

However, overestimation of spot areas and touching spots

still remain to some extent We will tackle these problems

by a strategy for sharpening the fuzziness of the peroxisome

cluster, an aspect-ratio criterion and quadtree decomposition,

which are presented in the following subsections

Focusing image spots by sharpening fuzzy regions

Based on the concept of a fuzzy set (Zadeh, 1965) and the

notion of the Shannon’s entropy (Shannon and Weaver, 1948),

the measure of fuzziness of a fuzzy set was initially defined

by DeLuca and Termini (1972) as follows:

(1) The fuzziness of A = 0 if A is a crisp set, i.e µ A (x)∈

{0, 1}, ∀x ∈ X.

(2) The fuzziness of A is maximum when µA (x)= 0.5,

∀x ∈ X.

(3) The fuzziness of A is greater than or equal to that of A∗

if A∗is a sharpened version of A, i.e µ∗

A (x) ≥ µ A (x)

if µ A (x) ≥ 0.5; and µ∗

A (x) ≤ µ A (x) if µ A (x)≤ 0.5

Let µ P ( x) be the fuzzy membership grade that indicates how

a possible pixel x belongs to the set containing all the

per-oxisome images, we then apply the notion of the measure of fuzziness to sharpen the fuzzy region of interest (peroxisome)

by defining

µ∗

P ( x)=



1 µ P ( x) ≥ δ µ

where 0.5 < δ µ <1 is a fuzzy membership threshold

What we discuss next is how to get an appropriate value for

δ µin order to obtain good sharpened peroxisome spots which can make the task of isolating touching spots easier To fix a

concrete idea, let µc∗( x) be the fuzzy membership grade of a

pixel x belonging to the peroxisome cluster c∗ We can say that

an optimal value of c∗must be some value between the least,

denoted by fmin(x |c∗) and the most, denoted by f

max(x |c∗),

bright intensities which are to be assigned to c∗ Of course, it is

difficult to determine fmin(x |c∗) readily; however, f

max(x |c∗)

is immediately available, i.e by checking the membership

grade of the brightest pixel of the whole image assigned to c∗

given by the FCM We therefore select δ = µc∗(x∗), where

f (x∗) is the maximum intensity value, because µc∗(x∗) rep-resents the brightest and the least bright pixels which are to

be assigned to c∗ Finally, each segmented peroxisome region will be filled up in case there are any holes in the region This

is because there exist some low-intensity pixels within the regions It is also mentioned, as in the problem under study, that the fluoresence-processed puncta are always brighter than any other objects (background and noise represented by

fluor-escence stain) Therefore, selecting the brightest pixel for δ µ

will not be affected by noise and outliers

Figure 5 shows an improved segmentation version, in com-parison with the result as shown in Figure 4 By applying the sharpening procedure defined in Equation (4)—the segmented spot areas are sharpened and brought closer to the real spot areas than the former segmented results; in addition, more outliers are removed in this sharpened version

Isolating touching spots by aspect-ratio criterion

We define an aspect ratio of a spot image p, based on which

touching spots can be isolated, as

r(p)= wmin(p)

wmax(p), where wmin(p) and wmax(p)are the minimum and maximum

widths of the spot area and wmin(p)≥ the maximum width

of the estimated smallest spot size

Fig 5 Segmentation of image A by sharpening FCM with three

clusters

The procedure for splitting touching spots is described as

follows

(1) Given a spot image p i , i = 1, , I, where I is the

number of segmented spots which are greater than an

estimated smallest spot image

(2) If r(p i ) < 0.5, then split p i into two subimages p1i and

p2i at the location of wmin(p i )

(a) If p g i , g= 1, 2, is greater than an estimated

smal-lest spot size and r(p i g ) < 0.5, then separate p i j

into two subimages p g i,1 and p i g,2 at the location

of wmin(p i

g )

(b) Repeat step (a) for all subimages p g i , ,Gwhere each

subscript takes the values from 1 to 2

(3) Repeat steps 1 and 2 for all p i

Adaptive segmentation by quadtree partition

What has been described above regarding the fuzzy

member-ship threshold δ µexpressed in Equation (4) is a nonadaptive

case for the FCM-based segmentation because δ µremains the

same for the whole image We notice that, first, the regions of

interest (peroxisome) occupy only part of the image; second,

if we apply the FCM to segment these images with a large

size of 1392× 1040 pixels, the computational time will be

considerably long and not so effective for real applications;

and third, as an important factor regarding the parameter δµ

whose sensitivity depends on the brightest pixel and if the

brightest pixel is not chosen locally, then many real spots

having relatively low intensities will be subjected to false

rejection We therefore apply the scheme of quadtree

parti-tion that has been largely used for fractal image compression

(Fisher, 1994), to iteratively divide the whole image into

quad-rants so that both segmentation quality and speed will be much

enhanced, particularly the second and third issues By doing

this, the segmentation now becomes an adaptive process in

which the threshold δµwill be estimated differently for each image quadrant

The image will be partitioned into quadrants (upper left, upper right, lower left and lower right) if its variance is equal

or greater than a splitting threshold δvar, that is

var= 1

N

N

n=1

[f (x, y) − ¯ f (x , y)]2 ≥ δvar, (5)

where N is the total number of pixels within a (sub)image,

f (x , y) and ¯ f (x , y) are the pixel intensity and the average

pixel intensities of the (sub)image, respectively

In order to avoid carrying out the FCM-based segmenta-tion of subregions containing all background pixels, we define

another decision parameter, denoted as δseg, based on which the FCM-based segmentation will be performed if the max-imum intensity value within a subimage is greater than a threshold, i.e the decision is to do the fuzzy segmentation if

fmax(x , y) ≥ δseg, (6)

where fmax(x , y) is the maximum intensity value within a par-ticular subimage respectively, and δsegcan be experimentally estimated

Procedure for extracting peroxisome spots

(1) Convert the given RBG image into intensity imageI.

(2) Use the quadtree technique to partitionI into a set of

Qsubimages:I = I1∪ I2∪ · · · ∪ I Q (3) Do FCM-based segmentation for each I k, k =

1, , K, where K is the number of quadtree-split images which contain peroxisome spot(s), i.e K ≤ Q.

(4) Sharpen and fill up spot areas (if there are any holes)

(5) Isolate touching spots in eachI q , q = 1, , Q, using

the aspect-ratio criterion

(6) Assemble all segmented versions ofI q , q = 1, , Q

to obtain the whole segmented version ofI.

RESULTS AND DISCUSSION

In addition to the illustrations, which have been presented

in the foregoing sections, showing some advantages of our FCM-based segmentation approach, we further test our pro-posed method and compare the results with other methods for image spot extraction For the current FCM analysis, we

select α = 2 and δseg to be the round off of (255/2) for all cases, for extracting peroxisome image spots on several real

images The reason for choosing the value of α= 2 is based

on the most popular choice for the FCM analysis found in literature as there is no certain analytical ground for selecting the right value of this parameter at present (Bezdek, 1981;

Chi et al., 1996) and for δsegbeing half of 255 is based on

pre-experiment on a few images from which δsegwas found

Fig 6 Original image B.

Fig 7 Segmentation of image B by Otsu’s thresholding.

fairly constant and only large discrepancy on the values of this

parameter will turn on or turn off the decision for the FCM

analysis

Figure 6 shows the intensity version of an RGB color

image (412× 357) that contains fluorescent-stained

perox-isome spots Edges of these spots are fuzzy due to low

contrast, also some of the spots are connected to each other

Some fluorescent stains may misrepresent spots (false spots)

for simple segmentation methods Figures 7–10 show the

segmented versions using Otsu thresholding method, FCM

with three clusters, ImageJ that is a public-domain image

processing software and can be downloaded from the web

(http://rsb.info.nih.gov/ij/) and our proposed FCM-based

seg-mentation method It can be seen from these figures that

the results obtained from both Otsu’s thresholding,

straight-forward FCM and ImageJ that uses a thresholding method

developed by Ridler and Calvard (1978), show false as well

Fig 8 Segmentation of image B by FCM with three clusters.

Fig 9 Segmentation of image B by ImageJ (iterative thresholding).

Fig 10 Segmentation of image B by proposed FCM-based method.

Fig 11 Original image C.

Fig 12 Segmentation of image C by Otsu’s thresholding.

Fig 13 Segmentation of image C by FCM with three clusters.

as overestimated peroxisome spots; whereas our proposed

method yields the segmentation results that are quite close

to the actual spots and can also isolate touching spots

As another experiment, Figure 11 shows the original image

where the task of spot extraction is more difficult than the

earlier case, in that the image contains many noisy spots

Figures 12–15 show the segmented versions using Otsu’s

Fig 14 Segmentation of image C by ImageJ (iterative thresholding).

Fig 15 Segmentation of image C by proposed FCM-based method.

thresholding method, FCM with three clusters, ImageJ and the proposed FCM-based segmentation The result obtained

by our approach is more accurate than the other three methods Few small fading peroxisome spots are omitted by our method whereas relatively large number of false spots are detected by the other three methods, particularly by Otsu’s thresholding and the ImageJ

Figures 16–17 shows the Canny edges (Canny, 1986) of the results obtained from ImageJ (Figure 14) and the proposed method (Figure 15), respectively Again it can be seen that the edges of the peroxisome spots obtained by our method are much more realistic than those of the ImageJ Spot areas obtained from the ImageJ are significantly overestimated from the actual spot sizes shown in Figure 11; whereas the proposed FCM-based segmentation approach yields a more accurate result with the spot areas being close to the actual spots Touching spots are also isolated by the proposed FCM-based method

Figures 18–20 show the full-size (1392× 1040) versions

of the original image, ImageJ-based and the proposed FCM-based segmentation results respectively Not only is the proposed method able to yield more accurate spot areas, but also able to suppress noise and isolate touching spots

Fig 16 Canny-edge image of segmentation by ImageJ (iterative

thresholding)

FCM-based method

Fig 18 Original image D.

Figures 21–23 show the full-size (1392× 1040) versions

of another original image, ImageJ-based, and the proposed

FCM-based segmentation results, respectively Conclusion

for this case are the same as stated above for the results shown

in Figures 18–20

thresholding)

Fig 20 Segmentation of image D by proposed FCM-based method.

Fig 21 Original image E.

It is mentioned that from all of the above presented res-ults, the extraction of the number of spots and the spot sizes obtained by our method gained the most favor of several biolo-gists at the Eskitis Institute for Cell and Molecular Therapies and the School of Biomolecular and Biomedical Sciences,

Fig 22 Segmentation of image E by ImageJ (iterative thresholding).

Fig 23 Segmentation of image E by proposed FCM-based method.

Griffith University From various results, the method is

reas-onably robust against noise as many low-contrast puncta

were detected, isolated and their sizes were more accurately

estimated than the other methods

CONCLUSIONS

We have presented an effective algorithm for extracting

fluor-escent peroxisome puncta in fuzzy images where the contrast

is low, spots are touching and background is mixed with

fluorescence, which make standard techniques for image

seg-mentation or edge detection ineffective We have tested our

proposed FCM-based algorithm with real image data and

obtained favorable results and in all cases have superior

res-ults in comparison with existing methods This algorithm

is expected to prove useful for the analysis of different cell compartments following fluorescence microscopy

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